The recent financial crisis and its aftermath boost the research of economic policy uncertainty and its relevant topics. In this paper, we forecast the oil return risks based on the CAViaR method and further depict the dynamic and heterogeneous features during the crisis (or non-crisis) period, as well as in different markets via DCC-GARCH models. The empirical results show the linkage of economic policy uncertainty and oil return risks, indicating an increasing trend and stronger relationship with major events. Further study shows the heterogeneous feature existing during crisis or non-crisis period, and there is heterogeneity in values and variations of their linkage in different markets. Therefore, policymakers should intervene timely in the crude oil market, release good news, and stabilize oil prices during the crisis period. During the non-crisis period, however, investors need to rationally analyze the price trend of the oil market, thereby preventing possible risks in the market.